time-to-botec

Benchmark sampling in different programming languages
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README.md (4087B)

      1 <!--
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      3 @license Apache-2.0
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      5 Copyright (c) 2018 The Stdlib Authors.
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      7 Licensed under the Apache License, Version 2.0 (the "License");
      8 you may not use this file except in compliance with the License.
      9 You may obtain a copy of the License at
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     11    http://www.apache.org/licenses/LICENSE-2.0
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     13 Unless required by applicable law or agreed to in writing, software
     14 distributed under the License is distributed on an "AS IS" BASIS,
     15 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     16 See the License for the specific language governing permissions and
     17 limitations under the License.
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     19 -->
     20 
     21 # Cumulative Distribution Function
     22 
     23 > [Discrete uniform][discrete-uniform-distribution] distribution [cumulative distribution function][cdf].
     24 
     25 <section class="intro">
     26 
     27 The [cumulative distribution function][cdf] for a [discrete uniform][discrete-uniform-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:discrete_uniform_cdf" align="center" raw="F(x)= \begin{cases} 0 & \text{for }x < a \\ \frac{\lfloor x \rfloor - a + 1}{b-a+1} & \text{for }a \le x < b \\ 1 & \text{for }x \ge b \end{cases}" alt="Cumulative distribution function for a discrete uniform distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="F(x)= \begin{cases} 0 &amp; \text{for }x &lt; a \\ \frac{\lfloor x \rfloor - a + 1}{b-a+1} &amp; \text{for }a \le x &lt; b \\ 1 &amp; \text{for }x \ge b \end{cases}" data-equation="eq:discrete_uniform_cdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/discrete-uniform/cdf/docs/img/equation_discrete_uniform_cdf.svg" alt="Cumulative distribution function for a discrete uniform distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `a` is the minimum support and `b` is the maximum support. The parameters must satisfy `a <= b`.
     39 
     40 </section>
     41 
     42 <!-- /.intro -->
     43 
     44 <section class="usage">
     45 
     46 ## Usage
     47 
     48 ```javascript
     49 var cdf = require( '@stdlib/stats/base/dists/discrete-uniform/cdf' );
     50 ```
     51 
     52 #### cdf( x, a, b )
     53 
     54 Evaluates the [cumulative distribution function][cdf] (CDF) for a [discrete uniform][discrete-uniform-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).
     55 
     56 ```javascript
     57 var y = cdf( 9.0, 0, 10 );
     58 // returns ~0.909
     59 
     60 y = cdf( 0.5, -2, 2 );
     61 // returns ~0.6
     62 
     63 y = cdf( -Infinity, 2, 4 );
     64 // returns 0.0
     65 
     66 y = cdf( Infinity, 2, 4 );
     67 // returns 1.0
     68 ```
     69 
     70 If `a` or `b` is not an integer value, the function returns `NaN`.
     71 
     72 ```javascript
     73 var y = cdf( 0.2, 1, 5.5 );
     74 // returns NaN
     75 
     76 y = cdf( NaN, 0, 1 );
     77 // returns NaN
     78 
     79 y = cdf( 0.0, NaN, 1 );
     80 // returns NaN
     81 
     82 y = cdf( 0.0, 0, NaN );
     83 // returns NaN
     84 ```
     85 
     86 If provided `a > b`, the function returns `NaN`.
     87 
     88 ```javascript
     89 var y = cdf( 0.5, 3, 2);
     90 // returns NaN
     91 ```
     92 
     93 #### cdf.factory( a, b )
     94 
     95 Returns a function for evaluating the [cumulative distribution function][cdf] of a [discrete uniform][discrete-uniform-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).
     96 
     97 ```javascript
     98 var mycdf = cdf.factory( 0, 10 );
     99 var y = mycdf( 0.5 );
    100 // returns ~0.091
    101 
    102 y = mycdf( 8.0 );
    103 // returns ~0.818
    104 ```
    105 
    106 </section>
    107 
    108 <!-- /.usage -->
    109 
    110 <section class="examples">
    111 
    112 ## Examples
    113 
    114 <!-- eslint no-undef: "error" -->
    115 
    116 ```javascript
    117 var randint = require( '@stdlib/random/base/discrete-uniform' );
    118 var randu = require( '@stdlib/random/base/randu' );
    119 var cdf = require( '@stdlib/stats/base/dists/discrete-uniform/cdf' );
    120 
    121 var randa = randint.factory( 0, 10 );
    122 var randb = randint.factory();
    123 var a;
    124 var b;
    125 var x;
    126 var v;
    127 var i;
    128 
    129 for ( i = 0; i < 10; i++ ) {
    130     x = randu() * 15.0;
    131     a = randa();
    132     b = randb( a, a+randa() );
    133     v = cdf( x, a, b );
    134     console.log( 'x: %d, a: %d, b: %d, F(x;a,b): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
    135 }
    136 ```
    137 
    138 </section>
    139 
    140 <!-- /.examples -->
    141 
    142 <section class="links">
    143 
    144 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
    145 
    146 [discrete-uniform-distribution]: https://en.wikipedia.org/wiki/Discrete_uniform_distribution
    147 
    148 </section>
    149 
    150 <!-- /.links -->